scholarly journals An efficient time algorithm for makespan objectives

2015 ◽  
Vol 5 (2) ◽  
pp. 75-80
Author(s):  
Yucel Ozturkoglu
Keyword(s):  
Processing Time ◽  
Single Machine Scheduling ◽  
Time Interval ◽  
Main Question ◽  
Scheduling Problems ◽  
Automatic Production ◽  
Polynomial Time Algorithms ◽  
Automatic Production Line ◽  
One Machine ◽  
Machine Deterioration

This paper focuses on a single machine scheduling subject to machine deterioration with rate-modifying activities (RMA). The motivation for this study stems from the automatic-production line problem with one machine. The main question is to find the sequence in which jobs should be scheduled, how many maintenance activity (RMA) to use, if any, and where to insert them in the schedule during the time interval with optimal makespan objective. This problem is known to be NP-hard and we give concise analyses of the problem and provide polynomial time algorithms to solve the makespan problem. We also propose an algorithm which can be applied to some scheduling problems with the actual processing time of job nonlinearly based on its position.This paper focuses on a single machine scheduling subject to machine deterioration with rate-modifying activities (RMA). The motivation for this study stems from the automatic-production line problem with one machine. The main question is to find the sequence in which jobs should be scheduled, how many maintenance activity (RMA) to use, if any, and where to insert them in the schedule during the time interval with optimal makespan objective. This problem is known to be NP-hard and we give concise analyses of the problem and provide polynomial time algorithms to solve the makespan problem. We also propose an algorithm which can be applied to some scheduling problems with the actual processing time of job nonlinearly based on its position.

SINGLE MACHINE SCHEDULING WITH A LEARNING EFFECT AND A RATE-MODIFYING ACTIVITY

2011 ◽  
Vol 28 (04) ◽  
pp. 511-521 ◽  
Author(s):  
CHUANLI ZHAO ◽  
HENGYONG TANG
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Learning Effect ◽  
Window Size ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Polynomial Time Algorithms ◽  
Due Window ◽  
Machine Scheduling Problems

In the paper, single machine scheduling problems with a learning effect and a rate-modifying activity are considered. Under the learning effect, the processing time of a job is a decreasing function of its position in the sequence. The rate-modifying activity is an event that can change the speed of the machine, and hence the processing time of jobs after the activity. The following objective functions are considered: the makespan, the total earliness, tardiness and completion time penalty, and the total earliness, tardiness, due-window starting time and due-window size penalty. Polynomial time algorithms are proposed to optimally solve the problems.

Scheduling with Rejection and a Deteriorating Maintenance Activity on a Single Machine

2017 ◽  
Vol 34 (02) ◽  
pp. 1750010 ◽  
Author(s):  
Shi-Sheng Li ◽  
Ren-Xia Chen
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Single Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problems ◽  
Maintenance Activity ◽  
Polynomial Time Algorithms ◽  
Deteriorating Maintenance ◽  
The Impact

We study single-machine scheduling problems with job rejection and a deteriorating maintenance activity, where the impact of performing this activity is reflected in a reduction of the job processing times. The duration of the maintenance activity is a linear increasing function of its starting time. The aim is to determine the location of the maintenance activity and the job sequence of the accepted jobs so as to minimize scheduling cost of the accepted jobs plus total penalty of the rejected jobs. When the scheduling measures are the makespan, total completion time and combination of earliness, tardiness and due date cost, we provide polynomial time algorithms to solve these problems, respectively. When the scheduling measures are the maximum tardiness and total weighted completion time under the agreeable ratio assumption, we introduce pseudo-polynomial time algorithms to solve these [Formula: see text]-hard problems, respectively.

scholarly journals Due Date Single Machine Scheduling Problems with Nonlinear Deterioration and Learning Effects and Past Sequence Dependent Setup Times

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Hüseyin Ceylan
Keyword(s):  
Processing Time ◽  
Single Machine Scheduling ◽  
Setup Times ◽  
Scheduling Problems ◽  
Due Dates ◽  
Sequence Dependent ◽  
Special Cases ◽  
Sequence Dependent Setup ◽  
Dependent Setup Times ◽  
Sequence Dependent Setup Times

We present some problems against due dates with nonlinear learning and deterioration effects and past sequence dependent setup times. In this study, two effects (learning and deterioration) are used for the same processing time. The processing time of a job is shorter if it is scheduled later, rather than in the sequence. This phenomenon is known in the literature as a “learning effect.” On the other hand, in many realistic scheduling settings, a job processed later consumes more time than the same job processed earlier—this is known as scheduling with deteriorating jobs. In the past sequence dependent setup times approach, the setup time of a job is proportionate to the sum of processing times of the jobs already scheduled. In this study, we demonstrated that some problems with due dates remain polynomially solvable. However, for some other problems, we concentrated on finding polynomially solves under their special cases.

Robust Single Machine Scheduling with Stochastic Processing Times Based on Event Point

2014 ◽  
Vol 668-669 ◽  
pp. 1641-1645
Author(s):  
Xiao Xia He ◽  
Chun Yao ◽  
Qiu Hua Tang
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Model Base ◽  
Processing Times ◽  
Robust Model ◽  
Stochastic Processing ◽  
Stochastic Processing Times

The scheduling of the single machine is of major importance in applications. The focus of this work is to analyze the scheduling problems in single-machine scheduling in the presence of uncertain parameters. By assuming that the processing time is represented by the nominal value plus a perturbation, we propose a robust model base on event point, and we obtain the feasible job sequence with some probability confidence level.

scholarly journals Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects

2019 ◽  
Vol 23 (6) ◽  
pp. 665-680
Author(s):  
Alan J. Soper ◽  
Vitaly A. Strusevich
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Cumulative Effect ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Priority Rules ◽  
Optimal Sequence ◽  
Positional Effect ◽  
Wide Range ◽  
Completion Times

AbstractWe address single-machine scheduling problems for which the actual processing times of jobs are subject to various effects, including a positional effect, a cumulative effect and their combination. We review the known results on the problems to minimize the makespan, the sum of the completion times and their combinations and identify the problems for which an optimal sequence cannot be found by simple priority rules such as Shortest Processing Time (SPT) and/or Longest Processing Time (LPT). Typically, these are problems to minimize the sum of the completion times under a deterioration effect, and we verify under which conditions for these problems an optimal permutation is V-shaped (an LPT subsequence followed by an SPT subsequence). We demonstrate that previously used techniques for proving that an optimal sequence is V-shaped are not properly justified. We use the corrected method to describe a wide range of problems with a pure positional effect and a combination of a cumulative effect with a positional effect for which an optimal sequence is V-shaped. On the other hand, we show that even the refined approach has its limitations.

Multiprocessor Flow Shop Scheduling Problem with Common due Window

2013 ◽  
Vol 284-287 ◽  
pp. 3712-3716 ◽  
Author(s):  
Rong Hwa Huang ◽  
Tung Han Yu ◽  
Chang Lin Yang
Keyword(s):  
Flow Shop ◽  
Capacity Utilization ◽  
Flow Shop Scheduling ◽  
Time Interval ◽  
Scheduling Problems ◽  
Work In Process ◽  
Due Windows ◽  
Due Window ◽  
Weighted Earliness ◽  
One Machine

The objective of scheduling is to maximize capacity utilization, minimize work-in-process inventory and ensure timely delivery. The due windows problem proposes that jobs should only be finished within the time interval that meets customer needs. This research applies integer programming (IP) and ant colony optimization (ACO) to solve due window problems in a flow shop with multiprocessors (FSMP). To improve the performance of jobs within due windows, this research splits them into different numbers of processing lots so they can be processed on more than one machine simultaneously. This shortens the total weighted earliness and tardiness of the jobs. The ACO is applied as a heuristic tool for solving the scheduling problems, and the solution results show that ACO has good validity, robustness and effectiveness.

Common Due Window Assignment Scheduling with Proportional Linear Deterioration Effects

2020 ◽  
Vol 37 (01) ◽  
pp. 1950031
Author(s):  
Xue Huang ◽  
Na Yin ◽  
Wei-Wei Liu ◽  
Ji-Bo Wang
Keyword(s):  
Window Size ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Polynomial Time Algorithms ◽  
Linear Deterioration ◽  
Optimality Properties ◽  
Due Window ◽  
Tardy Jobs ◽  
Machine Scheduling Problems ◽  
Due Window Assignment

In this paper, single-machine scheduling problems with proportional linear deterioration effects and common due window assignment simultaneously are considered. Two different objective functions are studied, the first is to minimize the sum of the number of early jobs, number of tardy jobs and due window location and due window size, the second is to minimize the sum of the earliness cost, tardiness cost, due window location and due window size. Optimality properties for all problems are provided and polynomial time algorithms for solving these problems are given.

scholarly journals Minimizing the Makespan for Scheduling Problems with General Deterioration Effects

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xianyu Yu ◽  
Yulin Zhang ◽  
Kai Huang
Keyword(s):  
Processing Time ◽  
Flow Shop ◽  
Single Machine Scheduling ◽  
Flow Shop Scheduling ◽  
Scheduling Problems ◽  
Shop Scheduling ◽  
Processing Times ◽  
Polynomially Solvable ◽  
Machine Scheduling Problems ◽  
Normal Processing

This paper investigates the scheduling problems with general deterioration models. By the deterioration models, the actual processing time functions of jobs depend not only on the scheduled position in the job sequence but also on the total weighted normal processing times of the jobs already processed. In this paper, the objective is to minimize the makespan. For the single-machine scheduling problems with general deterioration effects, we show that the considered problems are polynomially solvable. For the flow shop scheduling problems with general deterioration effects, we also show that the problems can be optimally solved in polynomial time under the proposed conditions.

scholarly journals Two-Agent Single-Machine Scheduling with Resource-Dependent Starting Times

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Peng Liu ◽  
Xiaoyu Tian
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Single Machine Scheduling ◽  
Resource Consumption ◽  
Scheduling Problems ◽  
Starting Time ◽  
Polynomial Time Algorithms ◽  
Agent Scheduling ◽  
Optimal Polynomial

We consider several two-agent scheduling problems with resource consumption on a single machine, where each of the agents wants to minimize a measure dependent on its own jobs. The starting time of each job of the first agent is related to the amount of resource consumed. The objective is to minimize the total amount of resource consumption of the first agent with the restriction that the makespan or the total completion time of the second agent cannot exceed a given boundU. The optimal properties and the optimal polynomial time algorithms are proposed to solve the scheduling problems.

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